$ \left(\dfrac{81}{16}\right)^{-\frac{1}{4}}$
$= \left(\dfrac{16}{81}\right)^{\frac{1}{4}}$ Figure out what goes in the blank: $\Big(? \Big)^{4}=\dfrac{16}{81}$ Figure out what goes in the blank: $\Big({\dfrac{2}{3}}\Big)^{4}=\dfrac{16}{81}$ So $\left(\dfrac{81}{16}\right)^{-\frac{1}{4}}=\left(\dfrac{16}{81}\right)^{\frac{1}{4}}=\dfrac{2}{3}$